A conventional diffuser for volatile material, such as a volatile aromatic or chemical agent has a vapor-permeable casing made of ethylene-vinyl acetate (EVA) resin, and a volatile material such as a volatile aromatic or chemical liquid is enclosed in the inner space of the casing. This diffuser diffuses the volatile constituent of the agent into a surrounding air through the casing by taking advantage of vapor permeability derived from the molecular structure of EVA. It takes several hours to allow the volatile constituent to be diffused into the surrounding air through the EVA resin casing. This slow response is defective from the viewpoint of practicability. In addition, the casing undesirably deforms due to the reduced volume of the liquid caused by the volatilization of the volatile constituent, resulting in deteriorated appearance.